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Mathematics Department

Combinatorics, Algebra, & Topology Seminar

Fall 2020


All talks are on google Meet at the specific Meet address.

  • Nov
    09
  • The geometry of parabolic Hamiltonian reduction
    Mee Seong Im
    USNA
    Time: 03:45 PM

    View Abstract

    n the construction of Hamiltonian reductions in symplectic geometry, rich connections to Hilbert schemes, Calogero-Moser spaces, and rational spherical Cherednik algebras have emerged. A parabolic analogue of the classical general linear group construction (realized after a reduction from the cotangent bundle of enhanced partial Grothendieck-Springer resolutions) potentially opens doors for its connections to isospectral Hilbert schemes, partial flag Hilbert schemes, and other algebraic varieties that are important in geometric representation theory, algebraic combinatorics, and quantum topology. Our construction can also be realized by certain (partial) quiver flag varieties, appearing in the geometric interplay in quiver Hecke algebras that categorify quantum groups. I will discuss a parabolic analogue of the cotangent bundle of the extended general linear Lie algebra, discussing the complete intersection of the zero fiber of a moment map, an enumeration of the irreducible components, and a parabolic analog of an almost-commuting scheme appearing in the study of Calogero-Moser systems. I will end with conjectures on their birationality of their geometric invariant theory (GIT) quotient, which depends on the stability condition, to well-known Hilbert schemes.
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